TSTP Solution File: KRS104+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS104+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:44:46 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS104+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 09:43:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(ra_Px2_type, type, (
% 0.20/0.41 ra_Px2: ( $i * $i ) > $o)).
% 0.20/0.41 tff(i2003_11_14_17_20_50869_type, type, (
% 0.20/0.41 i2003_11_14_17_20_50869: $i)).
% 0.20/0.41 tff(cc_type, type, (
% 0.20/0.41 cc: $i > $o)).
% 0.20/0.41 tff(tptp_fun_Y0_4_type, type, (
% 0.20/0.41 tptp_fun_Y0_4: $i > $i)).
% 0.20/0.41 tff(ccxcomp_type, type, (
% 0.20/0.41 ccxcomp: $i > $o)).
% 0.20/0.41 tff(ra_Px8_type, type, (
% 0.20/0.41 ra_Px8: ( $i * $i ) > $o)).
% 0.20/0.41 tff(ca_Cx8xcomp_type, type, (
% 0.20/0.41 ca_Cx8xcomp: $i > $o)).
% 0.20/0.41 tff(tptp_fun_Y0_13_type, type, (
% 0.20/0.41 tptp_fun_Y0_13: $i > $i)).
% 0.20/0.41 tff(cb_type, type, (
% 0.20/0.41 cb: $i > $o)).
% 0.20/0.41 tff(tptp_fun_Y_12_type, type, (
% 0.20/0.41 tptp_fun_Y_12: $i > $i)).
% 0.20/0.41 tff(ca_Cx8_type, type, (
% 0.20/0.41 ca_Cx8: $i > $o)).
% 0.20/0.41 tff(ca_Cx7_type, type, (
% 0.20/0.41 ca_Cx7: $i > $o)).
% 0.20/0.41 tff(ca_Cx6_type, type, (
% 0.20/0.41 ca_Cx6: $i > $o)).
% 0.20/0.41 tff(cUnsatisfiablexcomp_type, type, (
% 0.20/0.41 cUnsatisfiablexcomp: $i > $o)).
% 0.20/0.41 tff(ra_Px5_type, type, (
% 0.20/0.41 ra_Px5: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y0_1_type, type, (
% 0.20/0.41 tptp_fun_Y0_1: $i > $i)).
% 0.20/0.41 tff(cUnsatisfiable_type, type, (
% 0.20/0.41 cUnsatisfiable: $i > $o)).
% 0.20/0.41 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.41 tptp_fun_Y_0: $i > $i)).
% 0.20/0.41 tff(ra_Px7_type, type, (
% 0.20/0.41 ra_Px7: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y_11_type, type, (
% 0.20/0.41 tptp_fun_Y_11: $i > $i)).
% 0.20/0.41 tff(ca_Cx7xcomp_type, type, (
% 0.20/0.41 ca_Cx7xcomp: $i > $o)).
% 0.20/0.41 tff(ca_type, type, (
% 0.20/0.41 ca: $i > $o)).
% 0.20/0.41 tff(cbxcomp_type, type, (
% 0.20/0.41 cbxcomp: $i > $o)).
% 0.20/0.41 tff(ca_Cx1_type, type, (
% 0.20/0.41 ca_Cx1: $i > $o)).
% 0.20/0.41 tff(tptp_fun_Y_5_type, type, (
% 0.20/0.41 tptp_fun_Y_5: $i > $i)).
% 0.20/0.41 tff(tptp_fun_Y0_10_type, type, (
% 0.20/0.41 tptp_fun_Y0_10: $i > $i)).
% 0.20/0.41 tff(ra_Px6_type, type, (
% 0.20/0.41 ra_Px6: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y_8_type, type, (
% 0.20/0.41 tptp_fun_Y_8: $i > $i)).
% 0.20/0.41 tff(ca_Cx6xcomp_type, type, (
% 0.20/0.41 ca_Cx6xcomp: $i > $o)).
% 0.20/0.41 tff(tptp_fun_Y0_9_type, type, (
% 0.20/0.41 tptp_fun_Y0_9: $i > $i)).
% 0.20/0.41 tff(ra_Px3_type, type, (
% 0.20/0.41 ra_Px3: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y0_2_type, type, (
% 0.20/0.41 tptp_fun_Y0_2: $i > $i)).
% 0.20/0.41 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.41 tptp_fun_Y_3: $i > $i)).
% 0.20/0.41 tff(1,assumption,(ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869))), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[X: $i] : refl((~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))) <=> (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (^[X: $i] : rewrite((~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))) <=> (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (^[X: $i] : trans(monotonicity(rewrite((ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))) <=> (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))), ((((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X))) & (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))) <=> (((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X))) & (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))), rewrite((((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X))) & (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))) <=> (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))), ((((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X))) & (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))) <=> (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![X: $i] : (((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X))) & (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))) <=> ![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (![X: $i] : (ca_Cx8xcomp(X) <=> ?[Y0: $i] : ra_Px8(X, Y0)) <=> ![X: $i] : (ca_Cx8xcomp(X) <=> ?[Y0: $i] : ra_Px8(X, Y0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(10,axiom,(![X: $i] : (ca_Cx8xcomp(X) <=> ?[Y0: $i] : ra_Px8(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_21')).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![X: $i] : (ca_Cx8xcomp(X) <=> ?[Y0: $i] : ra_Px8(X, Y0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.42 tff(12,plain,(
% 0.20/0.42 ![X: $i] : (((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X))) & (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[11])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 ((~![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))) | (~((~((~ca_Cx8xcomp(i2003_11_14_17_20_50869)) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y0_13(i2003_11_14_17_20_50869)))) | (~(ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (~((~((~ca_Cx8xcomp(i2003_11_14_17_20_50869)) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y0_13(i2003_11_14_17_20_50869)))) | (~(ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (((~((~ca_Cx8xcomp(i2003_11_14_17_20_50869)) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y0_13(i2003_11_14_17_20_50869)))) | (~(ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))))) | (ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (^[X: $i] : refl((ca_Cx8xcomp(X) <=> (~((~cb(X)) | (~cc(X))))) <=> (ca_Cx8xcomp(X) <=> (~((~cb(X)) | (~cc(X))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![X: $i] : (ca_Cx8xcomp(X) <=> (~((~cb(X)) | (~cc(X))))) <=> ![X: $i] : (ca_Cx8xcomp(X) <=> (~((~cb(X)) | (~cc(X)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (^[X: $i] : rewrite((ca_Cx8xcomp(X) <=> (cc(X) & cb(X))) <=> (ca_Cx8xcomp(X) <=> (~((~cb(X)) | (~cc(X))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![X: $i] : (ca_Cx8xcomp(X) <=> (cc(X) & cb(X))) <=> ![X: $i] : (ca_Cx8xcomp(X) <=> (~((~cb(X)) | (~cc(X)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (![X: $i] : (ca_Cx8xcomp(X) <=> (cc(X) & cb(X))) <=> ![X: $i] : (ca_Cx8xcomp(X) <=> (cc(X) & cb(X)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(24,axiom,(![X: $i] : (ca_Cx8xcomp(X) <=> (cc(X) & cb(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_22')).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![X: $i] : (ca_Cx8xcomp(X) <=> (cc(X) & cb(X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.42 tff(26,plain,(
% 0.20/0.42 ![X: $i] : (ca_Cx8xcomp(X) <=> (cc(X) & cb(X)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[25])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (![X: $i] : (ca_Cx8xcomp(X) <=> (~((~cb(X)) | (~cc(X)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![X: $i] : (ca_Cx8xcomp(X) <=> (~((~cb(X)) | (~cc(X)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 ((~![X: $i] : (ca_Cx8xcomp(X) <=> (~((~cb(X)) | (~cc(X)))))) | (ca_Cx8xcomp(i2003_11_14_17_20_50869) <=> (~((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (ca_Cx8xcomp(i2003_11_14_17_20_50869) <=> (~((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.42 tff(31,assumption,(~ccxcomp(i2003_11_14_17_20_50869)), introduced(assumption)).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (^[X: $i] : refl((ccxcomp(X) | (~cb(X))) <=> (ccxcomp(X) | (~cb(X))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (![X: $i] : (ccxcomp(X) | (~cb(X))) <=> ![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![X: $i] : (ccxcomp(X) | (~cb(X))) <=> ![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (^[X: $i] : rewrite((cb(X) => ccxcomp(X)) <=> (ccxcomp(X) | (~cb(X))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![X: $i] : (cb(X) => ccxcomp(X)) <=> ![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.42 tff(37,axiom,(![X: $i] : (cb(X) => ccxcomp(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_7')).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.42 tff(40,plain,(
% 0.20/0.42 ![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[39])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (((~![X: $i] : (ccxcomp(X) | (~cb(X)))) | (ccxcomp(i2003_11_14_17_20_50869) | (~cb(i2003_11_14_17_20_50869)))) <=> ((~![X: $i] : (ccxcomp(X) | (~cb(X)))) | ccxcomp(i2003_11_14_17_20_50869) | (~cb(i2003_11_14_17_20_50869)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 ((~![X: $i] : (ccxcomp(X) | (~cb(X)))) | (ccxcomp(i2003_11_14_17_20_50869) | (~cb(i2003_11_14_17_20_50869)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ((~![X: $i] : (ccxcomp(X) | (~cb(X)))) | ccxcomp(i2003_11_14_17_20_50869) | (~cb(i2003_11_14_17_20_50869))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (~cb(i2003_11_14_17_20_50869)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[44, 41, 31])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) | cb(i2003_11_14_17_20_50869)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 ((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 ((~(ca_Cx8xcomp(i2003_11_14_17_20_50869) <=> (~((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))))) | (~ca_Cx8xcomp(i2003_11_14_17_20_50869)) | (~((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 ((~(ca_Cx8xcomp(i2003_11_14_17_20_50869) <=> (~((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))))) | (~ca_Cx8xcomp(i2003_11_14_17_20_50869))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (~ca_Cx8xcomp(i2003_11_14_17_20_50869)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[49, 30])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 ((~(ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0)))) | ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 ((~(ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0)))) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[52, 18])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (^[X: $i] : refl((cUnsatisfiablexcomp(X) <=> (~((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))))) <=> (cUnsatisfiablexcomp(X) <=> (~((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![X: $i] : (cUnsatisfiablexcomp(X) <=> (~((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))))) <=> ![X: $i] : (cUnsatisfiablexcomp(X) <=> (~((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (^[X: $i] : rewrite((cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X))) <=> (cUnsatisfiablexcomp(X) <=> (~((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X))) <=> ![X: $i] : (cUnsatisfiablexcomp(X) <=> (~((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X))) <=> ![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (^[X: $i] : rewrite((cUnsatisfiablexcomp(X) <=> ((ca_Cx7(X) & ca_Cx8(X)) & ca_Cx6(X))) <=> (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (![X: $i] : (cUnsatisfiablexcomp(X) <=> ((ca_Cx7(X) & ca_Cx8(X)) & ca_Cx6(X))) <=> ![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.42 tff(61,axiom,(![X: $i] : (cUnsatisfiablexcomp(X) <=> ((ca_Cx7(X) & ca_Cx8(X)) & ca_Cx6(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_3')).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.42 tff(64,plain,(
% 0.20/0.42 ![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[63])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (![X: $i] : (cUnsatisfiablexcomp(X) <=> (~((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (![X: $i] : (cUnsatisfiablexcomp(X) <=> (~((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 ((~![X: $i] : (cUnsatisfiablexcomp(X) <=> (~((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X)))))) | (cUnsatisfiablexcomp(i2003_11_14_17_20_50869) <=> (~((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (cUnsatisfiablexcomp(i2003_11_14_17_20_50869) <=> (~((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (^[X: $i] : refl((~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))) <=> (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))) <=> ![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (^[X: $i] : rewrite((~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))) <=> (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))) <=> ![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))) <=> ![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (^[X: $i] : trans(monotonicity(rewrite((cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))) <=> (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))), ((((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X))) & (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))) <=> (((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X))) & (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))), rewrite((((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X))) & (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))) <=> (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))), ((((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X))) & (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))) <=> (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (![X: $i] : (((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X))) & (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))) <=> ![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (![X: $i] : (cUnsatisfiablexcomp(X) <=> ?[Y0: $i] : ra_Px5(X, Y0)) <=> ![X: $i] : (cUnsatisfiablexcomp(X) <=> ?[Y0: $i] : ra_Px5(X, Y0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(77,axiom,(![X: $i] : (cUnsatisfiablexcomp(X) <=> ?[Y0: $i] : ra_Px5(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_4')).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (![X: $i] : (cUnsatisfiablexcomp(X) <=> ?[Y0: $i] : ra_Px5(X, Y0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.42 tff(79,plain,(
% 0.20/0.42 ![X: $i] : (((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X))) & (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[78])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 ((~![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))) | (~((~((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))) | (~(cUnsatisfiablexcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y0))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (~((~((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))) | (~(cUnsatisfiablexcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y0)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (((~((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))) | (~(cUnsatisfiablexcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y0))))) | ((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 ((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.20/0.42 tff(86,assumption,(ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869))), introduced(assumption)).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (^[X: $i] : rewrite((~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))))) <=> (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))))) <=> ![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (^[X: $i] : refl((~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))))) <=> (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (^[X: $i] : rewrite((~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))))) <=> (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[92, 90])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (^[X: $i] : trans(monotonicity(rewrite(((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))) <=> ((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))), ((((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))) & (cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) <=> (((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))) & (cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))))), rewrite((((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))) & (cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) <=> (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))))))), ((((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))) & (cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) <=> (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (![X: $i] : (((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))) & (cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (![X: $i] : (cUnsatisfiable(X) <=> (~?[Y: $i] : ra_Px5(X, Y))) <=> ![X: $i] : (cUnsatisfiable(X) <=> (~?[Y: $i] : ra_Px5(X, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(97,axiom,(![X: $i] : (cUnsatisfiable(X) <=> (~?[Y: $i] : ra_Px5(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (![X: $i] : (cUnsatisfiable(X) <=> (~?[Y: $i] : ra_Px5(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.42 tff(99,plain,(
% 0.20/0.42 ![X: $i] : (((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))) & (cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[98])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))) | (~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[101, 88])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 ((~![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))))))) | (~((~(cUnsatisfiable(i2003_11_14_17_20_50869) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y_0(i2003_11_14_17_20_50869)))) | (~((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (~((~(cUnsatisfiable(i2003_11_14_17_20_50869) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y_0(i2003_11_14_17_20_50869)))) | (~((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (((~(cUnsatisfiable(i2003_11_14_17_20_50869) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y_0(i2003_11_14_17_20_50869)))) | (~((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))))) | ((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 ((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (cUnsatisfiable(i2003_11_14_17_20_50869) <=> cUnsatisfiable(i2003_11_14_17_20_50869)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(108,axiom,(cUnsatisfiable(i2003_11_14_17_20_50869)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_23')).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (cUnsatisfiable(i2003_11_14_17_20_50869)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 ((~((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y)))) | (~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 ((~((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y)))) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[111, 106])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 ((~![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))) | (~ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[113, 112, 86])).
% 0.20/0.42 tff(115,plain,(~ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 ((~((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))) | (~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 ((~((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))) | (~cUnsatisfiablexcomp(i2003_11_14_17_20_50869))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[117, 85])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 ((~(cUnsatisfiablexcomp(i2003_11_14_17_20_50869) <=> (~((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869)))))) | cUnsatisfiablexcomp(i2003_11_14_17_20_50869) | ((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 ((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[119, 118, 68])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (^[X: $i] : refl((ca_Cx7xcomp(X) <=> (~((~ca(X)) | (~cc(X))))) <=> (ca_Cx7xcomp(X) <=> (~((~ca(X)) | (~cc(X))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx7xcomp(X) <=> (~((~ca(X)) | (~cc(X))))) <=> ![X: $i] : (ca_Cx7xcomp(X) <=> (~((~ca(X)) | (~cc(X)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[121])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (^[X: $i] : rewrite((ca_Cx7xcomp(X) <=> (cc(X) & ca(X))) <=> (ca_Cx7xcomp(X) <=> (~((~ca(X)) | (~cc(X))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx7xcomp(X) <=> (cc(X) & ca(X))) <=> ![X: $i] : (ca_Cx7xcomp(X) <=> (~((~ca(X)) | (~cc(X)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[123])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx7xcomp(X) <=> (cc(X) & ca(X))) <=> ![X: $i] : (ca_Cx7xcomp(X) <=> (cc(X) & ca(X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(126,axiom,(![X: $i] : (ca_Cx7xcomp(X) <=> (cc(X) & ca(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_18')).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx7xcomp(X) <=> (cc(X) & ca(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.43 tff(128,plain,(
% 0.20/0.43 ![X: $i] : (ca_Cx7xcomp(X) <=> (cc(X) & ca(X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[127])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx7xcomp(X) <=> (~((~ca(X)) | (~cc(X)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx7xcomp(X) <=> (~((~ca(X)) | (~cc(X)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 ((~![X: $i] : (ca_Cx7xcomp(X) <=> (~((~ca(X)) | (~cc(X)))))) | (ca_Cx7xcomp(i2003_11_14_17_20_50869) <=> (~((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (ca_Cx7xcomp(i2003_11_14_17_20_50869) <=> (~((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (^[X: $i] : refl((~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))) <=> (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 (![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))) <=> ![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (^[X: $i] : rewrite((~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))) <=> (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))) <=> ![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))) <=> ![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[136, 134])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (^[X: $i] : trans(monotonicity(rewrite((cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))) <=> (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))), ((((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X))) & (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))) <=> (((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X))) & (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))), rewrite((((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X))) & (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))) <=> (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))), ((((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X))) & (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))) <=> (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 (![X: $i] : (((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X))) & (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))) <=> ![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 (![X: $i] : (cc(X) <=> ?[Y0: $i] : ra_Px2(X, Y0)) <=> ![X: $i] : (cc(X) <=> ?[Y0: $i] : ra_Px2(X, Y0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(141,axiom,(![X: $i] : (cc(X) <=> ?[Y0: $i] : ra_Px2(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_9')).
% 0.20/0.43 tff(142,plain,
% 0.20/0.43 (![X: $i] : (cc(X) <=> ?[Y0: $i] : ra_Px2(X, Y0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.43 tff(143,plain,(
% 0.20/0.43 ![X: $i] : (((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X))) & (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[142])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 (![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 (![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 ((~![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))) | (~((~((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))) | (~(cc(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y0))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(147,plain,
% 0.20/0.43 (~((~((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))) | (~(cc(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y0)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.43 tff(148,plain,
% 0.20/0.43 (((~((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))) | (~(cc(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y0))))) | ((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 ((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.20/0.43 tff(150,assumption,(~((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))), introduced(assumption)).
% 0.20/0.43 tff(151,plain,
% 0.20/0.43 (((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) | cc(i2003_11_14_17_20_50869)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(152,plain,
% 0.20/0.43 (cc(i2003_11_14_17_20_50869)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.20/0.43 tff(153,plain,
% 0.20/0.43 ((~((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))) | (~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(154,plain,
% 0.20/0.43 ((~((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.20/0.43 tff(155,plain,
% 0.20/0.43 (ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[154, 149])).
% 0.20/0.43 tff(156,plain,
% 0.20/0.43 (^[X: $i] : refl((ca_Cx1(X) <=> (~((~cbxcomp(X)) | (~ccxcomp(X))))) <=> (ca_Cx1(X) <=> (~((~cbxcomp(X)) | (~ccxcomp(X))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(157,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx1(X) <=> (~((~cbxcomp(X)) | (~ccxcomp(X))))) <=> ![X: $i] : (ca_Cx1(X) <=> (~((~cbxcomp(X)) | (~ccxcomp(X)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.43 tff(158,plain,
% 0.20/0.43 (^[X: $i] : rewrite((ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X))) <=> (ca_Cx1(X) <=> (~((~cbxcomp(X)) | (~ccxcomp(X))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(159,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X))) <=> ![X: $i] : (ca_Cx1(X) <=> (~((~cbxcomp(X)) | (~ccxcomp(X)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[158])).
% 0.20/0.43 tff(160,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X))) <=> ![X: $i] : (ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(161,axiom,(![X: $i] : (ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_11')).
% 0.20/0.43 tff(162,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.43 tff(163,plain,(
% 0.20/0.43 ![X: $i] : (ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[162])).
% 0.20/0.43 tff(164,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx1(X) <=> (~((~cbxcomp(X)) | (~ccxcomp(X)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.20/0.43 tff(165,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx1(X) <=> (~((~cbxcomp(X)) | (~ccxcomp(X)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.20/0.43 tff(166,plain,
% 0.20/0.43 ((~![X: $i] : (ca_Cx1(X) <=> (~((~cbxcomp(X)) | (~ccxcomp(X)))))) | (ca_Cx1(i2003_11_14_17_20_50869) <=> (~((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(167,plain,
% 0.20/0.43 (ca_Cx1(i2003_11_14_17_20_50869) <=> (~((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.20/0.43 tff(168,plain,
% 0.20/0.43 (((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) | ca(i2003_11_14_17_20_50869)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 (ca(i2003_11_14_17_20_50869)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[168, 150])).
% 0.20/0.43 tff(170,plain,
% 0.20/0.43 (^[X: $i] : refl((ca_Cx1(X) | (~ca(X))) <=> (ca_Cx1(X) | (~ca(X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(171,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx1(X) | (~ca(X))) <=> ![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx1(X) | (~ca(X))) <=> ![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(173,plain,
% 0.20/0.43 (^[X: $i] : rewrite((ca(X) => ca_Cx1(X)) <=> (ca_Cx1(X) | (~ca(X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 (![X: $i] : (ca(X) => ca_Cx1(X)) <=> ![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[173])).
% 0.20/0.43 tff(175,axiom,(![X: $i] : (ca(X) => ca_Cx1(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_5')).
% 0.20/0.43 tff(176,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.43 tff(177,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.20/0.43 tff(178,plain,(
% 0.20/0.43 ![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[177])).
% 0.20/0.43 tff(179,plain,
% 0.20/0.43 (![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.20/0.43 tff(180,plain,
% 0.20/0.43 (((~![X: $i] : (ca_Cx1(X) | (~ca(X)))) | (ca_Cx1(i2003_11_14_17_20_50869) | (~ca(i2003_11_14_17_20_50869)))) <=> ((~![X: $i] : (ca_Cx1(X) | (~ca(X)))) | ca_Cx1(i2003_11_14_17_20_50869) | (~ca(i2003_11_14_17_20_50869)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(181,plain,
% 0.20/0.43 ((~![X: $i] : (ca_Cx1(X) | (~ca(X)))) | (ca_Cx1(i2003_11_14_17_20_50869) | (~ca(i2003_11_14_17_20_50869)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(182,plain,
% 0.20/0.43 ((~![X: $i] : (ca_Cx1(X) | (~ca(X)))) | ca_Cx1(i2003_11_14_17_20_50869) | (~ca(i2003_11_14_17_20_50869))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.43 tff(183,plain,
% 0.20/0.43 (ca_Cx1(i2003_11_14_17_20_50869) | (~ca(i2003_11_14_17_20_50869))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[182, 179])).
% 0.20/0.43 tff(184,plain,
% 0.20/0.43 (ca_Cx1(i2003_11_14_17_20_50869)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[183, 169])).
% 0.20/0.43 tff(185,plain,
% 0.20/0.43 ((~(ca_Cx1(i2003_11_14_17_20_50869) <=> (~((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869)))))) | (~ca_Cx1(i2003_11_14_17_20_50869)) | (~((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(186,plain,
% 0.20/0.43 (~((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[185, 184, 167])).
% 0.20/0.43 tff(187,plain,
% 0.20/0.43 (((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))) | ccxcomp(i2003_11_14_17_20_50869)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(188,plain,
% 0.20/0.43 (ccxcomp(i2003_11_14_17_20_50869)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.20/0.43 tff(189,plain,
% 0.20/0.43 (^[X: $i] : rewrite((~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))))) <=> (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(190,plain,
% 0.20/0.43 (![X: $i] : (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))))) <=> ![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.43 tff(191,plain,
% 0.20/0.43 (^[X: $i] : refl((~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))))) <=> (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(192,plain,
% 0.20/0.43 (![X: $i] : (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))))) <=> ![X: $i] : (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[191])).
% 0.20/0.43 tff(193,plain,
% 0.20/0.43 (^[X: $i] : rewrite((~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))))) <=> (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(194,plain,
% 0.20/0.43 (![X: $i] : (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))))) <=> ![X: $i] : (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[193])).
% 0.20/0.43 tff(195,plain,
% 0.20/0.43 (![X: $i] : (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))))) <=> ![X: $i] : (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[194, 192])).
% 0.20/0.43 tff(196,plain,
% 0.20/0.43 (^[X: $i] : trans(monotonicity(rewrite(((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))) <=> ((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))), ((((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))) & (ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) <=> (((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))) & (ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))))), rewrite((((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))) & (ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) <=> (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X))))))), ((((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))) & (ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) <=> (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(197,plain,
% 0.20/0.43 (![X: $i] : (((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))) & (ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) <=> ![X: $i] : (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[196])).
% 0.20/0.43 tff(198,plain,
% 0.20/0.43 (![X: $i] : (ccxcomp(X) <=> (~?[Y: $i] : ra_Px2(X, Y))) <=> ![X: $i] : (ccxcomp(X) <=> (~?[Y: $i] : ra_Px2(X, Y)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(199,axiom,(![X: $i] : (ccxcomp(X) <=> (~?[Y: $i] : ra_Px2(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_10')).
% 0.20/0.43 tff(200,plain,
% 0.20/0.43 (![X: $i] : (ccxcomp(X) <=> (~?[Y: $i] : ra_Px2(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.20/0.43 tff(201,plain,(
% 0.20/0.43 ![X: $i] : (((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))) & (ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[200])).
% 0.20/0.43 tff(202,plain,
% 0.20/0.43 (![X: $i] : (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.20/0.43 tff(203,plain,
% 0.20/0.43 (![X: $i] : (~((~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))) | (~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[202, 195])).
% 0.20/0.43 tff(204,plain,
% 0.20/0.43 (![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[203, 190])).
% 0.20/0.43 tff(205,plain,
% 0.20/0.43 ((~![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))))))) | (~((~(ccxcomp(i2003_11_14_17_20_50869) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y_5(i2003_11_14_17_20_50869)))) | (~((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(206,plain,
% 0.20/0.43 (~((~(ccxcomp(i2003_11_14_17_20_50869) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y_5(i2003_11_14_17_20_50869)))) | (~((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.20/0.43 tff(207,plain,
% 0.20/0.43 (((~(ccxcomp(i2003_11_14_17_20_50869) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y_5(i2003_11_14_17_20_50869)))) | (~((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))))) | ((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(208,plain,
% 0.20/0.43 ((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.20/0.43 tff(209,plain,
% 0.20/0.43 ((~((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y)))) | (~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(210,plain,
% 0.20/0.43 ((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.20/0.43 tff(211,plain,
% 0.20/0.43 (![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[210, 188])).
% 0.20/0.43 tff(212,plain,
% 0.20/0.43 ((~![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))) | (~ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(213,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[212, 211, 155])).
% 0.20/0.44 tff(214,plain,((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(215,plain,
% 0.20/0.44 ((~(ca_Cx7xcomp(i2003_11_14_17_20_50869) <=> (~((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))))) | (~ca_Cx7xcomp(i2003_11_14_17_20_50869)) | (~((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(216,plain,
% 0.20/0.44 ((~(ca_Cx7xcomp(i2003_11_14_17_20_50869) <=> (~((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))))) | (~ca_Cx7xcomp(i2003_11_14_17_20_50869))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.20/0.44 tff(217,plain,
% 0.20/0.44 (~ca_Cx7xcomp(i2003_11_14_17_20_50869)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[216, 132])).
% 0.20/0.44 tff(218,plain,
% 0.20/0.44 (^[X: $i] : rewrite((~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))))) <=> (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(219,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))))) <=> ![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[218])).
% 0.20/0.44 tff(220,plain,
% 0.20/0.44 (^[X: $i] : refl((~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))))) <=> (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(221,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))))) <=> ![X: $i] : (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[220])).
% 0.20/0.44 tff(222,plain,
% 0.20/0.44 (^[X: $i] : rewrite((~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))))) <=> (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(223,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))))) <=> ![X: $i] : (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[222])).
% 0.20/0.44 tff(224,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))))) <=> ![X: $i] : (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[223, 221])).
% 0.20/0.44 tff(225,plain,
% 0.20/0.44 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))) <=> ((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))), ((((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))) & (ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) <=> (((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))) & (ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))))), rewrite((((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))) & (ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) <=> (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))))))), ((((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))) & (ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) <=> (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(226,plain,
% 0.20/0.44 (![X: $i] : (((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))) & (ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) <=> ![X: $i] : (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[225])).
% 0.20/0.44 tff(227,plain,
% 0.20/0.44 (![X: $i] : (ca_Cx7xcomp(X) <=> (~?[Y: $i] : ra_Px7(X, Y))) <=> ![X: $i] : (ca_Cx7xcomp(X) <=> (~?[Y: $i] : ra_Px7(X, Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(228,axiom,(![X: $i] : (ca_Cx7xcomp(X) <=> (~?[Y: $i] : ra_Px7(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_19')).
% 0.20/0.44 tff(229,plain,
% 0.20/0.44 (![X: $i] : (ca_Cx7xcomp(X) <=> (~?[Y: $i] : ra_Px7(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.20/0.44 tff(230,plain,(
% 0.20/0.44 ![X: $i] : (((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))) & (ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[229])).
% 0.20/0.44 tff(231,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.20/0.44 tff(232,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))) | (~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[231, 224])).
% 0.20/0.44 tff(233,plain,
% 0.20/0.44 (![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[232, 219])).
% 0.20/0.44 tff(234,plain,
% 0.20/0.44 ((~![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))))))) | (~((~(ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))) | (~((~ca_Cx7xcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(235,plain,
% 0.20/0.44 (~((~(ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))) | (~((~ca_Cx7xcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.20/0.44 tff(236,plain,
% 0.20/0.44 (((~(ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))) | (~((~ca_Cx7xcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y))))) | (ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(237,plain,
% 0.20/0.44 (ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.20/0.44 tff(238,plain,
% 0.20/0.44 ((~(ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))) | ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(239,plain,
% 0.20/0.44 (ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.20/0.44 tff(240,plain,
% 0.20/0.44 (ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[239, 217])).
% 0.20/0.44 tff(241,assumption,(![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))), introduced(assumption)).
% 0.20/0.44 tff(242,assumption,(ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))), introduced(assumption)).
% 0.20/0.44 tff(243,plain,
% 0.20/0.44 ((~![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))) | (~ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(244,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[243, 242, 241])).
% 0.20/0.44 tff(245,plain,((~![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))) | (~ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(246,plain,
% 0.20/0.44 (~![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[245, 240])).
% 0.20/0.44 tff(247,assumption,((~((~ca_Cx7(i2003_11_14_17_20_50869)) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y0_10(i2003_11_14_17_20_50869)))) | (~(ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))))), introduced(assumption)).
% 0.20/0.44 tff(248,plain,
% 0.20/0.44 (^[X: $i] : refl((~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))) <=> (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(249,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[248])).
% 0.20/0.44 tff(250,plain,
% 0.20/0.44 (^[X: $i] : rewrite((~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))) <=> (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(251,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[250])).
% 0.20/0.44 tff(252,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[251, 249])).
% 0.20/0.44 tff(253,plain,
% 0.20/0.44 (^[X: $i] : trans(monotonicity(rewrite((ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))) <=> (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))), ((((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X))) & (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))) <=> (((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X))) & (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))), rewrite((((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X))) & (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))) <=> (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))), ((((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X))) & (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))) <=> (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(254,plain,
% 0.20/0.44 (![X: $i] : (((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X))) & (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))) <=> ![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[253])).
% 0.20/0.44 tff(255,plain,
% 0.20/0.44 (![X: $i] : (ca_Cx7(X) <=> ?[Y0: $i] : ra_Px7(X, Y0)) <=> ![X: $i] : (ca_Cx7(X) <=> ?[Y0: $i] : ra_Px7(X, Y0))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(256,axiom,(![X: $i] : (ca_Cx7(X) <=> ?[Y0: $i] : ra_Px7(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_17')).
% 0.20/0.44 tff(257,plain,
% 0.20/0.44 (![X: $i] : (ca_Cx7(X) <=> ?[Y0: $i] : ra_Px7(X, Y0))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.20/0.44 tff(258,plain,(
% 0.20/0.44 ![X: $i] : (((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X))) & (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[257])).
% 0.20/0.44 tff(259,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[258, 254])).
% 0.20/0.44 tff(260,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[259, 252])).
% 0.20/0.44 tff(261,plain,
% 0.20/0.44 ((~![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))) | (~((~((~ca_Cx7(i2003_11_14_17_20_50869)) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y0_10(i2003_11_14_17_20_50869)))) | (~(ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(262,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[261, 260, 247])).
% 0.20/0.44 tff(263,plain,(~((~((~ca_Cx7(i2003_11_14_17_20_50869)) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y0_10(i2003_11_14_17_20_50869)))) | (~(ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(264,plain,
% 0.20/0.44 (((~((~ca_Cx7(i2003_11_14_17_20_50869)) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y0_10(i2003_11_14_17_20_50869)))) | (~(ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))))) | (ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(265,plain,
% 0.20/0.44 (ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.20/0.44 tff(266,plain,
% 0.20/0.44 ((~(ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0)))) | ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(267,plain,
% 0.20/0.44 (ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[266, 265])).
% 0.20/0.44 tff(268,plain,
% 0.20/0.44 (ca_Cx7(i2003_11_14_17_20_50869)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[267, 246])).
% 0.20/0.44 tff(269,plain,
% 0.20/0.44 (^[X: $i] : refl((~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))) <=> (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(270,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[269])).
% 0.20/0.44 tff(271,plain,
% 0.20/0.44 (^[X: $i] : rewrite((~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))) <=> (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(272,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[271])).
% 0.20/0.44 tff(273,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[272, 270])).
% 0.20/0.44 tff(274,plain,
% 0.20/0.44 (^[X: $i] : trans(monotonicity(rewrite((ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))) <=> (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))), ((((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X))) & (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))) <=> (((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X))) & (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))), rewrite((((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X))) & (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))) <=> (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))), ((((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X))) & (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))) <=> (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(275,plain,
% 0.20/0.44 (![X: $i] : (((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X))) & (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))) <=> ![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[274])).
% 0.20/0.44 tff(276,plain,
% 0.20/0.44 (![X: $i] : (ca_Cx6xcomp(X) <=> ?[Y0: $i] : ra_Px6(X, Y0)) <=> ![X: $i] : (ca_Cx6xcomp(X) <=> ?[Y0: $i] : ra_Px6(X, Y0))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(277,axiom,(![X: $i] : (ca_Cx6xcomp(X) <=> ?[Y0: $i] : ra_Px6(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_16')).
% 0.20/0.44 tff(278,plain,
% 0.20/0.44 (![X: $i] : (ca_Cx6xcomp(X) <=> ?[Y0: $i] : ra_Px6(X, Y0))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.20/0.44 tff(279,plain,(
% 0.20/0.44 ![X: $i] : (((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X))) & (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[278])).
% 0.20/0.44 tff(280,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[279, 275])).
% 0.20/0.44 tff(281,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[280, 273])).
% 0.20/0.44 tff(282,plain,
% 0.20/0.44 ((~![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))) | (~((~((~ca_Cx6xcomp(i2003_11_14_17_20_50869)) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y0_9(i2003_11_14_17_20_50869)))) | (~(ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(283,plain,
% 0.20/0.44 (~((~((~ca_Cx6xcomp(i2003_11_14_17_20_50869)) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y0_9(i2003_11_14_17_20_50869)))) | (~(ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.20/0.44 tff(284,plain,
% 0.20/0.44 (((~((~ca_Cx6xcomp(i2003_11_14_17_20_50869)) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y0_9(i2003_11_14_17_20_50869)))) | (~(ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))))) | (ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(285,plain,
% 0.20/0.44 (ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[284, 283])).
% 0.20/0.44 tff(286,plain,
% 0.20/0.44 (^[X: $i] : refl((ca_Cx6xcomp(X) <=> (~((~ca(X)) | (~cb(X))))) <=> (ca_Cx6xcomp(X) <=> (~((~ca(X)) | (~cb(X))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(287,plain,
% 0.20/0.44 (![X: $i] : (ca_Cx6xcomp(X) <=> (~((~ca(X)) | (~cb(X))))) <=> ![X: $i] : (ca_Cx6xcomp(X) <=> (~((~ca(X)) | (~cb(X)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[286])).
% 0.20/0.44 tff(288,plain,
% 0.20/0.44 (^[X: $i] : rewrite((ca_Cx6xcomp(X) <=> (ca(X) & cb(X))) <=> (ca_Cx6xcomp(X) <=> (~((~ca(X)) | (~cb(X))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(289,plain,
% 0.20/0.44 (![X: $i] : (ca_Cx6xcomp(X) <=> (ca(X) & cb(X))) <=> ![X: $i] : (ca_Cx6xcomp(X) <=> (~((~ca(X)) | (~cb(X)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[288])).
% 0.20/0.44 tff(290,plain,
% 0.20/0.44 (![X: $i] : (ca_Cx6xcomp(X) <=> (ca(X) & cb(X))) <=> ![X: $i] : (ca_Cx6xcomp(X) <=> (ca(X) & cb(X)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(291,axiom,(![X: $i] : (ca_Cx6xcomp(X) <=> (ca(X) & cb(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_15')).
% 0.20/0.44 tff(292,plain,
% 0.20/0.44 (![X: $i] : (ca_Cx6xcomp(X) <=> (ca(X) & cb(X)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.20/0.44 tff(293,plain,(
% 0.20/0.44 ![X: $i] : (ca_Cx6xcomp(X) <=> (ca(X) & cb(X)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[292])).
% 0.20/0.44 tff(294,plain,
% 0.20/0.44 (![X: $i] : (ca_Cx6xcomp(X) <=> (~((~ca(X)) | (~cb(X)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.20/0.44 tff(295,plain,
% 0.20/0.44 (![X: $i] : (ca_Cx6xcomp(X) <=> (~((~ca(X)) | (~cb(X)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[294, 287])).
% 0.20/0.44 tff(296,plain,
% 0.20/0.44 ((~![X: $i] : (ca_Cx6xcomp(X) <=> (~((~ca(X)) | (~cb(X)))))) | (ca_Cx6xcomp(i2003_11_14_17_20_50869) <=> (~((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(297,plain,
% 0.20/0.44 (ca_Cx6xcomp(i2003_11_14_17_20_50869) <=> (~((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[296, 295])).
% 0.20/0.44 tff(298,plain,
% 0.20/0.44 ((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[187, 31])).
% 0.20/0.44 tff(299,plain,
% 0.20/0.44 ((~(ca_Cx1(i2003_11_14_17_20_50869) <=> (~((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869)))))) | (~ca_Cx1(i2003_11_14_17_20_50869))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[185, 298])).
% 0.20/0.44 tff(300,plain,
% 0.20/0.44 (~ca_Cx1(i2003_11_14_17_20_50869)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[299, 167])).
% 0.20/0.44 tff(301,plain,
% 0.20/0.44 (~ca(i2003_11_14_17_20_50869)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[182, 179, 300])).
% 0.20/0.44 tff(302,plain,
% 0.20/0.44 (((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))) | ca(i2003_11_14_17_20_50869)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(303,plain,
% 0.20/0.44 ((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[302, 301])).
% 0.20/0.44 tff(304,plain,
% 0.20/0.44 ((~(ca_Cx6xcomp(i2003_11_14_17_20_50869) <=> (~((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869)))))) | (~ca_Cx6xcomp(i2003_11_14_17_20_50869)) | (~((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(305,plain,
% 0.20/0.44 ((~(ca_Cx6xcomp(i2003_11_14_17_20_50869) <=> (~((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869)))))) | (~ca_Cx6xcomp(i2003_11_14_17_20_50869))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.20/0.44 tff(306,plain,
% 0.20/0.44 (~ca_Cx6xcomp(i2003_11_14_17_20_50869)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[305, 297])).
% 0.20/0.44 tff(307,plain,
% 0.20/0.44 ((~(ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0)))) | ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(308,plain,
% 0.20/0.44 ((~(ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0)))) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[307, 306])).
% 0.20/0.44 tff(309,plain,
% 0.20/0.44 (![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[308, 285])).
% 0.20/0.44 tff(310,assumption,(![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))), introduced(assumption)).
% 0.20/0.44 tff(311,assumption,(ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))), introduced(assumption)).
% 0.20/0.44 tff(312,plain,
% 0.20/0.44 ((~![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))) | (~ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(313,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[312, 311, 310])).
% 0.20/0.44 tff(314,plain,((~ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))) | (~![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(315,plain,
% 0.20/0.44 (~ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[314, 309])).
% 0.20/0.44 tff(316,plain,
% 0.20/0.44 (^[X: $i] : rewrite((~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))))) <=> (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(317,plain,
% 0.20/0.44 (![X: $i] : (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))))) <=> ![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[316])).
% 0.20/0.44 tff(318,plain,
% 0.20/0.44 (^[X: $i] : refl((~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))))) <=> (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(319,plain,
% 0.20/0.45 (![X: $i] : (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))))) <=> ![X: $i] : (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[318])).
% 0.20/0.45 tff(320,plain,
% 0.20/0.45 (^[X: $i] : rewrite((~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))))) <=> (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(321,plain,
% 0.20/0.45 (![X: $i] : (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))))) <=> ![X: $i] : (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[320])).
% 0.20/0.45 tff(322,plain,
% 0.20/0.45 (![X: $i] : (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))))) <=> ![X: $i] : (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[321, 319])).
% 0.20/0.45 tff(323,plain,
% 0.20/0.45 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))) <=> ((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))), ((((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))) & (ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) <=> (((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))) & (ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))))), rewrite((((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))) & (ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) <=> (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))))))), ((((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))) & (ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) <=> (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(324,plain,
% 0.20/0.45 (![X: $i] : (((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))) & (ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) <=> ![X: $i] : (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[323])).
% 0.20/0.45 tff(325,plain,
% 0.20/0.45 (![X: $i] : (ca_Cx6(X) <=> (~?[Y: $i] : ra_Px6(X, Y))) <=> ![X: $i] : (ca_Cx6(X) <=> (~?[Y: $i] : ra_Px6(X, Y)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(326,axiom,(![X: $i] : (ca_Cx6(X) <=> (~?[Y: $i] : ra_Px6(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_14')).
% 0.20/0.45 tff(327,plain,
% 0.20/0.45 (![X: $i] : (ca_Cx6(X) <=> (~?[Y: $i] : ra_Px6(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.20/0.45 tff(328,plain,(
% 0.20/0.45 ![X: $i] : (((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))) & (ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[327])).
% 0.20/0.45 tff(329,plain,
% 0.20/0.45 (![X: $i] : (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[328, 324])).
% 0.20/0.45 tff(330,plain,
% 0.20/0.45 (![X: $i] : (~((~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))) | (~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[329, 322])).
% 0.20/0.45 tff(331,plain,
% 0.20/0.45 (![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[330, 317])).
% 0.20/0.45 tff(332,plain,
% 0.20/0.45 ((~![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))))))) | (~((~(ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869)))) | (~((~ca_Cx6(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(333,plain,
% 0.20/0.45 (~((~(ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869)))) | (~((~ca_Cx6(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[332, 331])).
% 0.20/0.45 tff(334,plain,
% 0.20/0.45 (((~(ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869)))) | (~((~ca_Cx6(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y))))) | (ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(335,plain,
% 0.20/0.45 (ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[334, 333])).
% 0.20/0.45 tff(336,plain,
% 0.20/0.45 ((~(ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869)))) | ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(337,plain,
% 0.20/0.45 (ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[336, 335])).
% 0.20/0.45 tff(338,plain,
% 0.20/0.45 (ca_Cx6(i2003_11_14_17_20_50869)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[337, 315])).
% 0.20/0.45 tff(339,plain,
% 0.20/0.45 ((~((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869)))) | (~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(340,plain,
% 0.20/0.45 ((~((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869)))) | (~ca_Cx8(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[339, 338, 268])).
% 0.20/0.45 tff(341,plain,
% 0.20/0.45 (~ca_Cx8(i2003_11_14_17_20_50869)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[340, 120])).
% 0.20/0.45 tff(342,plain,
% 0.20/0.45 (^[X: $i] : rewrite((~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))))) <=> (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(343,plain,
% 0.20/0.45 (![X: $i] : (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))))) <=> ![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[342])).
% 0.20/0.45 tff(344,plain,
% 0.20/0.45 (^[X: $i] : refl((~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))))) <=> (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(345,plain,
% 0.20/0.45 (![X: $i] : (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))))) <=> ![X: $i] : (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[344])).
% 0.20/0.45 tff(346,plain,
% 0.20/0.45 (^[X: $i] : rewrite((~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))))) <=> (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(347,plain,
% 0.20/0.45 (![X: $i] : (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))))) <=> ![X: $i] : (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[346])).
% 0.20/0.45 tff(348,plain,
% 0.20/0.45 (![X: $i] : (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))))) <=> ![X: $i] : (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[347, 345])).
% 0.20/0.45 tff(349,plain,
% 0.20/0.45 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))) <=> ((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))), ((((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))) & (ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) <=> (((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))) & (ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))))), rewrite((((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))) & (ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) <=> (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))))))), ((((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))) & (ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) <=> (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(350,plain,
% 0.20/0.45 (![X: $i] : (((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))) & (ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) <=> ![X: $i] : (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[349])).
% 0.20/0.45 tff(351,plain,
% 0.20/0.45 (![X: $i] : (ca_Cx8(X) <=> (~?[Y: $i] : ra_Px8(X, Y))) <=> ![X: $i] : (ca_Cx8(X) <=> (~?[Y: $i] : ra_Px8(X, Y)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(352,axiom,(![X: $i] : (ca_Cx8(X) <=> (~?[Y: $i] : ra_Px8(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_20')).
% 0.20/0.45 tff(353,plain,
% 0.20/0.45 (![X: $i] : (ca_Cx8(X) <=> (~?[Y: $i] : ra_Px8(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.20/0.45 tff(354,plain,(
% 0.20/0.45 ![X: $i] : (((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))) & (ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[353])).
% 0.20/0.45 tff(355,plain,
% 0.20/0.45 (![X: $i] : (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[354, 350])).
% 0.20/0.45 tff(356,plain,
% 0.20/0.45 (![X: $i] : (~((~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))) | (~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[355, 348])).
% 0.20/0.45 tff(357,plain,
% 0.20/0.45 (![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[356, 343])).
% 0.20/0.45 tff(358,plain,
% 0.20/0.45 ((~![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))))))) | (~((~(ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))) | (~((~ca_Cx8(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(359,plain,
% 0.20/0.45 (~((~(ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))) | (~((~ca_Cx8(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[358, 357])).
% 0.20/0.45 tff(360,plain,
% 0.20/0.45 (((~(ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))) | (~((~ca_Cx8(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y))))) | (ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(361,plain,
% 0.20/0.45 (ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[360, 359])).
% 0.20/0.45 tff(362,plain,
% 0.20/0.45 ((~(ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))) | ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(363,plain,
% 0.20/0.45 (ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[362, 361])).
% 0.20/0.45 tff(364,plain,
% 0.20/0.45 (ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[363, 341])).
% 0.20/0.45 tff(365,plain,
% 0.20/0.45 ((~![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))) | (~ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(366,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[365, 364, 53])).
% 0.20/0.45 tff(367,plain,(ccxcomp(i2003_11_14_17_20_50869)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(368,plain,
% 0.20/0.45 (![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[210, 367])).
% 0.20/0.45 tff(369,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[212, 368, 1])).
% 0.20/0.45 tff(370,plain,(~ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(371,assumption,(~((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869)))), introduced(assumption)).
% 0.20/0.45 tff(372,plain,
% 0.20/0.45 (((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))) | cb(i2003_11_14_17_20_50869)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(373,plain,
% 0.20/0.45 (cb(i2003_11_14_17_20_50869)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[372, 371])).
% 0.20/0.45 tff(374,assumption,((~((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))) | (~(cb(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y0))))), introduced(assumption)).
% 0.20/0.45 tff(375,plain,
% 0.20/0.45 (^[X: $i] : refl((~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))) <=> (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(376,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))) <=> ![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[375])).
% 0.20/0.45 tff(377,plain,
% 0.20/0.45 (^[X: $i] : rewrite((~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))) <=> (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(378,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))) <=> ![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[377])).
% 0.20/0.45 tff(379,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))) <=> ![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[378, 376])).
% 0.20/0.45 tff(380,plain,
% 0.20/0.45 (^[X: $i] : trans(monotonicity(rewrite((cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))) <=> (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))), ((((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X))) & (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))) <=> (((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X))) & (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))), rewrite((((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X))) & (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))) <=> (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))), ((((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X))) & (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))) <=> (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(381,plain,
% 0.20/0.45 (![X: $i] : (((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X))) & (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))) <=> ![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[380])).
% 0.20/0.45 tff(382,plain,
% 0.20/0.45 (![X: $i] : (cb(X) <=> ?[Y0: $i] : ra_Px3(X, Y0)) <=> ![X: $i] : (cb(X) <=> ?[Y0: $i] : ra_Px3(X, Y0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(383,axiom,(![X: $i] : (cb(X) <=> ?[Y0: $i] : ra_Px3(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_6')).
% 0.20/0.45 tff(384,plain,
% 0.20/0.45 (![X: $i] : (cb(X) <=> ?[Y0: $i] : ra_Px3(X, Y0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.20/0.45 tff(385,plain,(
% 0.20/0.45 ![X: $i] : (((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X))) & (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[384])).
% 0.20/0.45 tff(386,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[385, 381])).
% 0.20/0.45 tff(387,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[386, 379])).
% 0.20/0.45 tff(388,plain,
% 0.20/0.45 ((~![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))) | (~((~((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))) | (~(cb(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y0))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(389,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[388, 387, 374])).
% 0.20/0.45 tff(390,plain,(~((~((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))) | (~(cb(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y0)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(391,plain,
% 0.20/0.45 (((~((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))) | (~(cb(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y0))))) | ((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(392,plain,
% 0.20/0.45 ((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[391, 390])).
% 0.20/0.45 tff(393,plain,
% 0.20/0.45 ((~((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))) | (~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(394,plain,
% 0.20/0.45 ((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[393, 392])).
% 0.20/0.45 tff(395,plain,
% 0.20/0.45 (ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[394, 373])).
% 0.20/0.45 tff(396,plain,
% 0.20/0.45 (ca(i2003_11_14_17_20_50869)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[302, 371])).
% 0.20/0.45 tff(397,plain,
% 0.20/0.45 (ca_Cx1(i2003_11_14_17_20_50869)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[183, 396])).
% 0.20/0.45 tff(398,plain,
% 0.20/0.45 ((~ca_Cx1(i2003_11_14_17_20_50869)) | (~((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[185, 167])).
% 0.20/0.45 tff(399,plain,
% 0.20/0.45 (~((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[398, 397])).
% 0.20/0.45 tff(400,plain,
% 0.20/0.45 (((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))) | cbxcomp(i2003_11_14_17_20_50869)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(401,plain,
% 0.20/0.45 (cbxcomp(i2003_11_14_17_20_50869)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[400, 399])).
% 0.20/0.45 tff(402,plain,
% 0.20/0.45 (^[X: $i] : rewrite((~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))))) <=> (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(403,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))))) <=> ![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[402])).
% 0.20/0.45 tff(404,plain,
% 0.20/0.45 (^[X: $i] : refl((~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))))) <=> (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(405,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))))) <=> ![X: $i] : (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[404])).
% 0.20/0.45 tff(406,plain,
% 0.20/0.45 (^[X: $i] : rewrite((~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))))) <=> (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(407,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))))) <=> ![X: $i] : (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[406])).
% 0.20/0.45 tff(408,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))))) <=> ![X: $i] : (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[407, 405])).
% 0.20/0.45 tff(409,plain,
% 0.20/0.45 (^[X: $i] : trans(monotonicity(rewrite(((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))) <=> ((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))), ((((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))) & (cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) <=> (((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))) & (cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))))), rewrite((((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))) & (cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) <=> (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))))))), ((((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))) & (cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) <=> (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(410,plain,
% 0.20/0.45 (![X: $i] : (((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))) & (cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) <=> ![X: $i] : (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[409])).
% 0.20/0.45 tff(411,plain,
% 0.20/0.45 (![X: $i] : (cbxcomp(X) <=> (~?[Y: $i] : ra_Px3(X, Y))) <=> ![X: $i] : (cbxcomp(X) <=> (~?[Y: $i] : ra_Px3(X, Y)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(412,axiom,(![X: $i] : (cbxcomp(X) <=> (~?[Y: $i] : ra_Px3(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_8')).
% 0.20/0.45 tff(413,plain,
% 0.20/0.45 (![X: $i] : (cbxcomp(X) <=> (~?[Y: $i] : ra_Px3(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.20/0.45 tff(414,plain,(
% 0.20/0.45 ![X: $i] : (((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))) & (cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[413])).
% 0.20/0.45 tff(415,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[414, 410])).
% 0.20/0.45 tff(416,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))) | (~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[415, 408])).
% 0.20/0.45 tff(417,plain,
% 0.20/0.45 (![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[416, 403])).
% 0.20/0.45 tff(418,plain,
% 0.20/0.45 ((~![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))))))) | (~((~(cbxcomp(i2003_11_14_17_20_50869) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y_3(i2003_11_14_17_20_50869)))) | (~((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(419,plain,
% 0.20/0.45 (~((~(cbxcomp(i2003_11_14_17_20_50869) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y_3(i2003_11_14_17_20_50869)))) | (~((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[418, 417])).
% 0.20/0.45 tff(420,plain,
% 0.20/0.45 (((~(cbxcomp(i2003_11_14_17_20_50869) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y_3(i2003_11_14_17_20_50869)))) | (~((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))))) | ((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(421,plain,
% 0.20/0.46 ((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[420, 419])).
% 0.20/0.46 tff(422,plain,
% 0.20/0.46 ((~((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y)))) | (~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(423,plain,
% 0.20/0.46 ((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[422, 421])).
% 0.20/0.46 tff(424,plain,
% 0.20/0.46 (![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[423, 401])).
% 0.20/0.46 tff(425,plain,
% 0.20/0.46 ((~![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))) | (~ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(426,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[425, 424, 395])).
% 0.20/0.46 tff(427,plain,((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(428,assumption,(~(ca_Cx6xcomp(i2003_11_14_17_20_50869) <=> (~((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869)))))), introduced(assumption)).
% 0.20/0.46 tff(429,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[296, 295, 428])).
% 0.20/0.46 tff(430,plain,(ca_Cx6xcomp(i2003_11_14_17_20_50869) <=> (~((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(431,plain,
% 0.20/0.46 ((~ca_Cx6xcomp(i2003_11_14_17_20_50869)) | (~((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[304, 430])).
% 0.20/0.46 tff(432,plain,
% 0.20/0.46 (~ca_Cx6xcomp(i2003_11_14_17_20_50869)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[431, 427])).
% 0.20/0.46 tff(433,assumption,((~((~ca_Cx6xcomp(i2003_11_14_17_20_50869)) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y0_9(i2003_11_14_17_20_50869)))) | (~(ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))))), introduced(assumption)).
% 0.20/0.46 tff(434,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[282, 281, 433])).
% 0.20/0.46 tff(435,plain,(~((~((~ca_Cx6xcomp(i2003_11_14_17_20_50869)) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y0_9(i2003_11_14_17_20_50869)))) | (~(ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(436,plain,
% 0.20/0.46 (ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[284, 435])).
% 0.20/0.46 tff(437,plain,
% 0.20/0.46 (ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[307, 436])).
% 0.20/0.46 tff(438,plain,
% 0.20/0.46 (![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[437, 432])).
% 0.20/0.46 tff(439,plain,
% 0.20/0.46 (~ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[314, 438])).
% 0.20/0.46 tff(440,plain,
% 0.20/0.46 (ca_Cx6(i2003_11_14_17_20_50869)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[337, 439])).
% 0.20/0.46 tff(441,assumption,(~(ca_Cx7xcomp(i2003_11_14_17_20_50869) <=> (~((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))))), introduced(assumption)).
% 0.20/0.46 tff(442,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[131, 130, 441])).
% 0.20/0.46 tff(443,plain,(ca_Cx7xcomp(i2003_11_14_17_20_50869) <=> (~((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(444,plain,
% 0.20/0.46 (~ca_Cx7xcomp(i2003_11_14_17_20_50869)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[216, 443])).
% 0.20/0.46 tff(445,plain,
% 0.20/0.46 (ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[239, 444])).
% 0.20/0.46 tff(446,plain,
% 0.20/0.46 (~![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[245, 445])).
% 0.20/0.46 tff(447,plain,
% 0.20/0.46 (ca_Cx7(i2003_11_14_17_20_50869)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[267, 446])).
% 0.20/0.46 tff(448,plain,
% 0.20/0.46 ((~((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869)))) | (~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[339, 447])).
% 0.20/0.46 tff(449,plain,
% 0.20/0.46 ((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[448, 120])).
% 0.20/0.46 tff(450,plain,
% 0.20/0.46 (~ca_Cx8(i2003_11_14_17_20_50869)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[449, 440])).
% 0.20/0.46 tff(451,plain,
% 0.20/0.46 (ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[363, 450])).
% 0.20/0.46 tff(452,assumption,(![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))), introduced(assumption)).
% 0.20/0.46 tff(453,assumption,(ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))), introduced(assumption)).
% 0.20/0.46 tff(454,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[365, 453, 452])).
% 0.20/0.46 tff(455,plain,((~![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))) | (~ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(456,plain,
% 0.20/0.46 (~![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[455, 451])).
% 0.20/0.46 tff(457,plain,
% 0.20/0.46 (ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[51, 18])).
% 0.20/0.46 tff(458,plain,
% 0.20/0.46 (ca_Cx8xcomp(i2003_11_14_17_20_50869)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[457, 456])).
% 0.20/0.46 tff(459,assumption,(~(ca_Cx8xcomp(i2003_11_14_17_20_50869) <=> (~((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))))), introduced(assumption)).
% 0.20/0.46 tff(460,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[29, 28, 459])).
% 0.20/0.46 tff(461,plain,(ca_Cx8xcomp(i2003_11_14_17_20_50869) <=> (~((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(462,plain,
% 0.20/0.46 ((~ca_Cx8xcomp(i2003_11_14_17_20_50869)) | (~((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[48, 461])).
% 0.20/0.46 tff(463,plain,
% 0.20/0.46 (~((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[462, 458])).
% 0.20/0.46 tff(464,plain,
% 0.20/0.46 (((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) | cc(i2003_11_14_17_20_50869)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(465,plain,
% 0.20/0.46 (cc(i2003_11_14_17_20_50869)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[464, 463])).
% 0.20/0.46 tff(466,plain,
% 0.20/0.46 (~((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[153, 465, 370])).
% 0.20/0.46 tff(467,plain,
% 0.20/0.46 ((~((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))) | (~(cc(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y0))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[148, 466])).
% 0.20/0.46 tff(468,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[146, 145, 467])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------